3. • All these network parameters relate total voltages and total
currents at each of the two ports.
• But at microwave frequency, these parameters can not be
used.
3
4. • At microwave frequency, two independent quantities
required for each waveguide terminal are an incident and
a reflected wave replacing voltage and current.
• Suppose that incident and reflected voltages waves on
the input guide are given in magnitude and phase at the
chosen reference plane by V1+ and V1-. Similarly incident
and reflected voltages waves on the reference plane two
is given by V2+ and V2-.
• It is common to normalize incident and reflected waves
as follows:
4
5. • The logical variables to use at the microwave
frequencies are travelling wave rather than total voltages
and total currents.
• These are S-parameters which are expressed as
5
6. • In general, the voltages at the terminals of the device
can be written as, Vn = an+bn.
• Scattering coefficients are then defined, such that the
voltage wave bi leaving the ‘i’ port owing to a voltage
wave aj incident upon the ‘j’ port when no waves enter
any of the other ports of the device is given by, bi=Sij aj.
• In general, when a voltage is incident upon all of the ‘n’
ports of the device, each incident voltage will make a
contribution to the total resultant voltage wave reflecting
from the ‘i’ port.
bi =Si1 a1 + Si2 a2+………..+ Sin an
6
7. • Now there are reflecting waves from ‘n’ ports, the set of
scattering equations
b1 =S11 a1 + S12 a2+………..+ S1n an
b2 =S21 a1 + S22 a2+………..+ S2n an
………………………………………………………………………
bn =Sn1 a1 + Sn2 a2+………..+ Snn an
• The diagonal element Sij of the scattering matrix is the
reflection coefficient at the ‘j’ port and represents the
reflected voltage wave which would be observed at this
port with an incident voltage wave of unit magnitude and
zero phase, when all the other ports are terminated in
matched impedances and hence no waves are reflected
back into the other ports.
7
8. Properties of S parameters
Consider the N-port network shown in Figure, where V+ is
the amplitude of the voltage wave incident on port n and V−
is the amplitude of the voltage wave reflected from port n.
8
9. The scattering matrix is defined as
A specific element of the scattering matrix can be
determined as
9
10. Reciprocal Networks and Lossless Networks
It can be shown that the scattering matrix for a reciprocal
network is symmetric, and that the scattering matrix for a
lossless network is unitary.
10
11. so the scattering matrix is symmetric for reciprocal
networks.If the network is lossless, no real power can be delivered to
the network. Thus, if the characteristic impedances of all the
ports are identical and assumed to be unity, the average
power delivered to the network is
11
12. For a lossless junction, the incident and reflected powers are
equal
so that, for
nonzero
A matrix that satisfies the above condition is called a unitary
matrix.
The matrix equation can be written in summation form as
If i = j
12
13. while if i = j
The above equations state that the dot product of any
column of [S] with the conjugate of that same column gives
unity, while the dot product of any column with the conjugate
of a different column gives zero (the columns are
orthonormal).
13
14. Waveguide Tees
E Plane tees:
Axis of its side arm is parallel to the E field
of the main guide
Collinear arms are symmetric about the
side arm
Input Output
Port 3- Port 1 and port 2 –
opposite
phase & same
magnitude (subtraction)
S13 = -S23 (both have signs)
MULTIPORT JUNCTION USED AS POWER COMBINER, POWER DIVIDER AND
POWER MONITORS
14
16. H Plane tees:
A waveguide tee in which the axis
of its side arm is perpendicular to
the E-field or parallel to the H-field of
the main guide.
Input Output
Port 3- Port 1 and port 2 –
same phase & same
magnitude (additive)
S13 = S23
16
19. Characteristics
1. If two waves of equal magnitude and the same
phase are fed into port 1 and port 2, the output
will be zero at port 3 and additive at port 4
2. If a wave is fed into port 4 (H arm), it will be
divided equally between port 1 and port 2 of the
collinear arms and will not appear at port 3 (E
arm).
3. If a wave is fed into port 3 (E arm), it will
produce an output of equal magnitude and
opposite phase at port 1 and port 2. Output at
port 4 is zero i.e S43 = S34 = 0.
19
20. 4. If a wave is fed into one of the collinear arms at
port 1 or port 2, it will not appear in the other
collinear arm at port 2 or port 1 because the E arm
causes a phase delay while the H arm causes the
phase advance. i.e S12 = S21 = 0.
S matrix of magic tee is
20
22. Directional coupler
• A directional coupler is a passive device which
couples part of the transmission power by a known
amount out through another port, often by using
two transmission lines set close enough together
such that energy passing through one is coupled to
the other.
• The device has four ports: input, transmitted,
coupled, and isolated. The term "main line" refers to
the section between ports 1 and 2.
• Common properties desired for all directional
couplers are wide operational bandwidth, high
directivity, and a good impedance match at all ports
when the other ports are terminated in matched
loads. 22
24. Bethe-hole directional coupler
• One of the most common, and simplest, waveguide directional couplers.
• This consists of two parallel waveguides, one stacked on top of the other, with a
hole between them.
• Some of the power from one guide is launched through the hole into the other.
24
Figure: Multi Hole Directional Coupler
25. Cont…
• The concept of the Bethe-hole coupler can be extended by
providing multiple holes. The holes are spaced λ/4 apart.
• The hole size is chosen to give the desired coupling between
two waveguides.
• Design criteria are to achieve a substantially flat coupling
together with high directivity over the desired band.
25
26. Properties of Directional Coupler
• A portion of power travelling from port 1 to port 2 is coupled to port 4
but does not go to port 3.
• A portion of power travelling from port 2 to port 1 is coupled to port 3
but does not go to port 4.
• Ports 1 and 3 are isolated and Ports 2 and 4 are isolated from each
other.
26
27. How does it separate the incident wave and
reflected wave for power measurements?
• Directivity is coupler's ability to separate the forward and backward
waves. That is separation of incident and reflected waves.
• Some part of Incident wave at port 1 goes to the port 4. because port 1
and 3 are isolated.
• Now if there are reflections from port 2 , that reflected wave will go to
port 3 only, because port 2 and 4 are isolated.
• So port 3 will have only part of reflected voltage and port 4 will have only
part of incident voltage.
27
28. Performance Parameters
• Coupling Factor: How much of incident power is being coupled for the measurement
purposes.
• Directivity: It is measure of how well the directional coupler distinguishes between
the forward and reverse travelling waves.
• Isolation: It is the sum of Coupling factor and Directivity in dB.
28
29. S-matrix of directional coupler
• In a directional coupler all four ports are completely matched. Thus the diagonal
elements of the S matrix are zero.
• There is no coupling between port 1 and port 3 and between port 2 and port 4, thus
29
30. • Thus the S matrix of the directional coupler becomes,
• Using the symmetry and unitary properties of S parameter, it
becomes
30
31. • Several types of directional coupler are exit. Such as a two
hole directional coupler, four hole directional coupler etc.
31
32. Isolator
RF isolator is a two port ferromagnetic
passive device which is used to protect other
RF components from excessive signal
reflection.
The interaction of the magnetic field to the
ferrite material inside isolators and circulators.
The rotary field is very strong and will cause
any RF/microwave signals in the frequency band
of interest at one port to follow the magnetic
flow to the adjacent port and not in the
opposite direction.
32
33. Farady’s Rotation Principle
• “The rotation of direction of E-field of a linearly polarized wave occurs
when passing through a ferrite medium.”
•When the wave travels
through one wavelength in
ferrite material ,E field vector
of LP wave rotates through
an angle given by,
33
35. Construction of Isolator
• It uses a Faraday rotation of 45°. For this
circular waveguide is used and a cylindrical
ferrite rod is placed along the axis of
circular waveguide.
• The ferrite rod is magnetized with static
magnetic field along the axis of waveguide.
• The circular waveguide is excited in
dominant mode TE11. Thus across the c/s
of the ferrite rod, field is linearly polarized.
• The length of ferrite rod and static magnetic
field is chosen such that E field vector gets
rotated by 45°.
35
36. Construction of Isolator
• At both the input and output ends, the circular waveguide is tapered to the
rectangular waveguide sections.
• The orientation of input and output rectangular waveguides are at 45° to each other.
• The resistive cards are placed near the input and output ports and they are parallel
to the broad walls of the rectangular sections.
• Resistive card at port 2 is also displaced 45° with respect to the input card.
36
37. Operation of Isolator
• A wave incident at port 1 has fixed E field direction. This excites TE11 mode in
circular waveguide.
• The E field of TE11 mode is perpendicular to the resistive card numbered 1.
hence power incident at port 1 is not affected by resistive card.
• Then wave encounters the magnetized ferrite rod and the direction of E field
gets rotated by 45° clockwise.
• Since the orientation of port 2 and resistive card 2 is fixed at angle of 45
clockwise to port 1, the E field remains perpendicular to the resistive card 2.
• Power transmitted from 1 to 2 remains unattenuated.
37
38. Cont.
• In 2nd case, the reflected signal will have E field direction such that it is unaffected
by resistive card 2.
• While travelling along ferrite rod , it will have rotation of 45 clockwise.
• After this rotation , E field lines become parallel to the resistive card 1 and power is
absorbed in this card.
• Therefore, power travelling from 2 to 1 gets completely attenuated inside the
isolator.
38
39. Circulator
• It is a 4-port microwave low power device which allows the power flow
only from port 1 to 2, or port 2 to 3, or port 3 to 4, or port 4 to1 in
clockwise direction.
39
41. Construction of 4-port Circulator
41
• It uses a magnetized ferrite rod to provide a 45° rotation of E
field with the same arrangement as that of isolator.
• No resistive cards are required, instead power is coupled out
to the required port.
• Ports 3 and 4 are oriented radially outward and are attached
to circular section.
• Ports 1, 2, 3 and 4 are oriented such that E field can couple to
these ports in numerical order after going through a rotation
of 45° in clockwise direction in each step.
43. Operation of 4-port Circulator
• For a signal TE10 incident at port 1, E field is in the direction of “m”.
• When the wave travels along a magnetized ferrite, the direction of E field gets
rotated by 45° and it coincides with the direction of “n”.
• So power incident at port 1 appears at port 2. It dose not coupled to port 3 and port
4, because E field is not significantly cut by these ports.
• Signal incident at port 2, gets rotated by 45° due to ferrite rode in clockwise
direction, and it coincides with the direction of “o”. So power incident at port2
comes out of port 3 only.
43
44. Applications of Circulator
44
• Duplexer for Radar Antenna
System
• Transmitter feeds the Antenna
while the received energy is
directed to the Rx.
• The high power transmitter can
be isolated from the sensitive
receiver.
• The same antenna can be used
for transmission & reception.
(Duplexer action)
46. 47
• These waveguide components are normally used to change the
direction of the guide through an arbitrary angle.
• E bend: the bend is in the direction of narrow wall dimension such
that lines of E field are affected.
• Bends have to be gradual to minimize the reflections.
• E-plane corner: At low frequencies, 90 bending are preferred.
• In order to minimize reflections from the discontinuities, it is
desirable to have the mean length “L”, between continuities equal to
an odd number of quarter-wave lengths, that is,
• If the mean length “L” is an odd number of quarter wavelengths, the
reflected waves from both ends of the waveguide section are
completely canceled.
• Waveguide twists are used to convert the vertical to horizontal
polarization and vice versa.
